Dormitories solved this problem.
There are also a few places without zoning regulations.
In the middle of a large, populous city --on land that is not part of a postsecondary institution-- you can't just build a dormitory on it.
You can rarely build anything over 2 stories on the coast in California. There's no political will for it, so nothing happens.
And construction on the coast is specifically restricted by law because that is the political will and has been for decades.
There absolutely are zoning restrictions that would prevent you from building a dormitory anywhere. Let me go buy a $10 million plot in La Jolla farms and try and put a dormitory on it. "Oh, but it's so close to UCSD", you might think... but the surrounding properties are all $20m+ single family homes (that's how it's zoned, after all) and the dorms would ruin the "community vibe".